Universal rigidity conjecture for generically globally rigid graphs

Let $d$ be a positive integer. A graph is generically globally rigid in dimension $d$ (or $d$-GGR) if a generic framework of the graph in $\mathbb{R}^d$ is uniquely determined up to Euclidean isometries by its edge lengths. A framework is generically universally rigid in dimension $d$ (or $d$-GUR) if it is generic in $\mathbb{R}^d$ and remains uniquely determined up to Euclidean isometries among frameworks in every Euclidean dimension.

Universal rigidity conjecture. Every $d$-GGR graph has a $d$-GUR framework.

The conjecture asks whether the global rigidity property of a graph guarantees the existence of a generic universally rigid realization. It is known in dimensions one and two, and for infinitely many $d$-GGR graphs when $d>2$, but the complete answer in higher dimensions remains open.